Problem: William is 3 times as old as Brandon. Eighteen years ago, William was 9 times as old as Brandon. How old is William now?
Answer: We can use the given information to write down two equations that describe the ages of William and Brandon. Let William's current age be $w$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $w = 3b$ Eighteen years ago, William was $w - 18$ years old, and Brandon was $b - 18$ years old. The information in the second sentence can be expressed in the following equation: $w - 18 = 9(b - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $b$ and substitute it into our second equation. Solving our first equation for $b$ , we get: $b = w / 3$ . Substituting this into our second equation, we get: $w - 18 = 9($ $(w / 3)$ $- 18)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 18 = 3 w - 162$ Solving for $w$ , we get: $2 w = 144$ $w = \dfrac{1}{2} \cdot 144 = 72$.